Energetics of two circular inclusions in anti-plane elastostatics

Abstract

In this paper, we use the recently derived solution of two circular elastic inclusions under anti-plane shear deformation ( Honein et al., 1992a, b) to evaluate the material forces, as well as expanding and rotating moments ‘acting’ on inclusions. These may be defined as the energy changes (e.g. energy release rates) accompanying unit translation, self-similar expansion and rotation of inclusions, respectively. The bond between the inclusions and the matrix is assumed to be perfect and the calculation is performed using the concept of the J, M and L path-independent integrals, respectively. The results obtained are valid under arbitrary loading. An illustrative example shows that two circular holes under remote uniform shear stress attract each other and that the J and M integrals grow without bound as the two holes become infinitely close. A careful examination of the expression for these integrals yields the result that the J and M integrals tend to infinity proportionally to 1/ ε , where ε is a non-dimensional distance between the holes. It is also noticed that the J integral decays rapidly to zero as the two holes become four or five radii apart. Other examples of two circular holes and inclusions under various stress fields are also considered and discussed.